* Prove and apply properties of parallelograms and rectangles. * Use properties of parallelograms and rectangles to solve problems.

1. 2.7.2 Parallelograms & Rectangles
The student is able to (I can):
• Prove and apply properties of parallelograms.
• Use properties of parallelograms to solve problems.
• Prove and apply properties of rectangles.
• Use properties of rectangles.

2. parallelogram
Properties of
Parallelograms
A quadrilateral with two pairs of parallel
sides.
Therefore, if a quadrilateral is a
parallelogram, then it has two pairs of
parallel sides.
>>
>>
T I
ME
TI ME, TE IM

3. Properties of
Parallelograms
If a quadrilateral is a parallelogram, then
opposite sides are congruent.
If a quadrilateral is a parallelogram, then
opposite angles are congruent.
KI NG, GK IN≅ ≅
K
NG
I
>>
>>
K
NG
O
∠K ≅ ∠N, ∠O ≅ ∠G

4. Properties of
Parallelograms
If a quadrilateral is a parallelogram, then
consecutive angles are supplementary.
If a quadrilateral is a parallelogram, then
its diagonals bisect each other.
1 2
34
m∠1 + m∠2 = 180°
m∠2 + m∠3 = 180°
m∠3 + m∠4 = 180°
m∠4 + m∠1 = 180°
>>
>>
T U
NE
SSSS
TS NS,ES US≅ ≅

5. Examples Find the value of the variable:
1. x =
2. x =
3. y =
5x + 3 2x + 15
4
(3x)º
(x + 84)º
yº
5x + 3 = 2x + 15
3x = 12
3x = x + 84
2x = 84
42
3(42) = 126º
y = 180 — 126
54

6. rectangle A parallelogram with four right angles.
If a parallelogram is a rectangle, then its
diagonals are congruent (“checking for
square”).
F I
SH
≅FS IH

7. Because a rectangle is a parallelogram, it
also “inherits” all of the properties of a
parallelogram:
• Opposite sides parallel
• Opposite sides congruent
• Opposite angles congruent (actually allallallall
angles are congruent)
• Consecutive angles supplementary
• Diagonals bisect each other

8. Example Find each length.
1. LW
LW = FO = 30
2. OL
OL = FW = 2(17) = 34
3. OW
∆OWL is a right triangle, so
OW = 16
F O
WL
30
17
+ =2 2 2
OW LW OL
+ =2
OW 900 1156
=2
OW 256
+ =2 2 2
OW 30 34